What is today about?

Reviewing common problems in applied work

Aligning theory, models, and estimation

Assume understand basics of conditional ignorability

Reciprocality

• Theories sometimes imply reciprocality
• Also sometimes an empirical problem
• But pretty much nothing is actually reciprocal; the world is recursive

Mechanisms and time

• Time enforces recursiveness
• Things that appear non-recursive are usually omitting mediators or time

Show 5 time DAG, 3 time SEM

Do another with a mechanism

Time DAG

Figure 1: ?(caption)

Time Estimator

Theory

• Make your theory recursive; use a DAG
• Estimation may requite non-recursive models

Temporal Order

• Illustrated by Vaisey & Miles (2019)

• If true model is \(y = \beta x_t + \alpha_i + e_{it}\) and you fit \(y = \beta^* x_{t-t} + \alpha_i + e_{it}\), \(E(\beta^*) = -0.5\beta\)

Example paper

Solutions

• Hard: Use strong theory to get timing right
• Use robust estimators, e.g., Allison#s approach
• If ambiguous contemporaneous path matters, you’ll need strong instrument(s)

Unobserved Heterogeneity

• Most common concern is stable traits
• Can’t just toss in fixed effects due to Nickell bias

Example paper

Solutions

• Different approaches
• Psychology approaches: RI-CLPM
• Econometric approaches: Arellano-Bond, ML-SEM

Low Temporal Variation

• \(Var(Y_2|Y_1) \rightarrow 0\) as \(\rho(Y_1,Y_2) \rightarrow 1\)
• Error becomes proportionally larger component
• Common with narrow waves, stable constructs

Example paper

That neighbs one? Hipp?

Solutions

• Error part can be dealt with using measurement models
  • Should do this anyway as outcomes are regressors, so measurement error attenuates estimates
• Address during data collection
  • Oversample for change
  • Look for shocks
• Consider different time lags or units of analysis
• Might be nothing you can do

Feedback and Questions

Contact:

Charles C. Lanfear
Institute of Criminology
University of Cambridge
cl948@cam.ac.uk